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Browse Prior Art Database

Anamorphic Afocal and Imaging Relay Lenses

IP.com Disclosure Number: IPCOM000105175D
Original Publication Date: 1993-Jun-01
Included in the Prior Art Database: 2005-Mar-19
Document File: 6 page(s) / 172K

Publishing Venue

IBM

Related People

Chastang, J: AUTHOR [+3]

Abstract

Disclosed is an optical system which is capable of: 1. imaging anamorphically a plane at infinity onto another plane at infinity 2. imaging anamorphically a plane at finite distance onto another plane at finite distance 3. transforming a parallel beam with a certain rectangular cross-section into another parallel beam with a different cross-section.

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Anamorphic Afocal and Imaging Relay Lenses

      Disclosed is an optical system which is capable of:

1.  imaging anamorphically a plane at infinity onto another plane at
    infinity

2.  imaging anamorphically a plane at finite distance onto another
    plane at finite distance
3.  transforming a parallel beam with a certain rectangular
    cross-section into another parallel beam with a different
    cross-section.

This optical system owing to its properties may be called an
anamorphic and afocal relay lens.

      This system in its simplest embodiment consists of two lenses.
A set of coordinate axes O xyz is attached to this system.  The axis
Oz is by definition the optical axis.  The surfaces of these lenses
are cylindrical or spherical.  They may thus be called
sphero-cylindrical.  If they are cylindrical the axis of the cylinder
is always oriented along the x axis or the y axis.  The lenses now
designated as  SC sub 1  and  SC sub 2 are first assumed to be
infinitely thin.  SC sub 1  and
 S C sub 2  are separated by a distance d as per Fig. 1.

      It can be shown that this system may be analyzed paraxially
(using for example the matrix formalism outlined in the references
listed below) exactly as if it consisted of two sub-systems which are
in effect given by the xOz section.  and the yOz section respectively
of the original system.  The first sub-system contained in the xOz
plane is shown on Fig. 2a.  The second sub-system contained in the
yOz plane is shown on Fig. 2b.  In the first case the focal lengths
of  SC sub 1  and SC2 are respectively  <f sub 1%x>  and
 <f sub 1%y> . In the second case the corresponding quantities are
<f sub 2%x>  and  <f sub 2%y> .

If the lens combination fulfills the double condition:

  <f sub 1%x>%+%<f sub 2%x>%=%d%%%'and'%%%<f sub 1%y>%+%<f sub
2%y>%=%d%%%%
                       eqno lbracket 1 rbracket
                                  %%.
it becomes afocal in both planes xOz and yOz.  In other words the
focii F sub 1 prime sub x  and F sub 1 prime sub y  of  SC sub 1 are
now coincident with the focii F sub 2 sub x  and F sub 2 sub y  of
SC sub 2  respectively.  An object at infinity will be re-imaged at
infinity.  However in addition to this infinity to infinity imaging
property it can be established that the proposed system is also
capable of finite distance imaging.  There exists two further planes,
and only two, between which optical conjugation is possible.  The
first of these planes, the object plane, is separated by a distance
t sub 1 from the first lens while the second plane, the image plane,
is separated by a distance  t sub 2  from the second lens, see Fig.
3.  The sign conventions used in Fig. 3 are important.  The following
formulas define  t sub 1  and  t sub 2 :

           <t sub 1>%=%<<d>%%<f sub 1%x>%%<f sub 1%y>> over
         <<f sub 1%y>%%<f...